https://file.aiquickdraw.com/mathbot/file/1729208731185cqx7ewmt.jpg

The question asks for the volume of a cylinder, and we are provided with the following dimensions:

- Height (\(h\)) = 13 cm
- Radius (\(r\)) = 7 cm

The formula for the volume of a cylinder is:

\[
V = \pi r^2 h
\]

### Step-by-step solution:

1. **Substitute the given values:**
   \[
   V = \pi \times (7^2) \times 13
   \]
   \[
   V = \pi \times 49 \times 13
   \]

2. **Calculate the result:**
   \[
   V = \pi \times 637
   \]
   \[
   V \approx 3.1416 \times 637 = 2001.64 \, \text{cm}^3
   \]

Thus, the volume of the cylinder, rounded to two decimal places, is:

\[
\boxed{2001.64 \, \text{cm}^3}
\]

Would you like more details or have any questions on this?

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Here are 5 related questions to expand on this:

1. What is the surface area of this cylinder?
2. How would the volume change if the radius were doubled?
3. How do you calculate the lateral surface area of a cylinder?
4. What would be the volume if the height were reduced by half?
5. How does changing the height affect the overall volume?

**Tip:** Always ensure you are consistent with units when solving geometry problems to avoid calculation errors.

Correct to two decimal places, this cylinder has a volume of: (with radius = 7 cm and height = 13 cm).

Find the volume of a cylinder with radius 7 cm and height 13 cm. Using the formula V = πr²h, we calculate the volume to be 2001.64 cubic centimeters, rounded to two decimal places. This problem helps students understand volume calculations for 3D shapes.

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